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1. A biomechanics-based parametrized cardiac end-diastolic pressure–volume relationship for accurate patient-specific calibration and estimation

Author

Dominique Chapelle and Arthur Le Gall

Subjects
Medicine, Science
Abstract

Abstract A simple power law has been proposed in the pioneering work of Klotz et al. (Am J Physiol Heart Circ Physiol 291(1):H403–H412, 2006) to approximate the end-diastolic pressure–volume relationship of the left cardiac ventricle, with limited inter-individual variability provided the volume is adequately normalized. Nevertheless, we use here a biomechanical model to investigate the sources of the remaining data dispersion observed in the normalized space, and we show that variations of the parameters of the biomechanical model realistically account for a substantial part of this dispersion. We therefore propose an alternative law based on the biomechanical model that embeds some intrinsic physical parameters, which directly enables personalization capabilities, and paves the way for related estimation approaches.

Published
2023
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2. Dimensional reduction of a poromechanical cardiac model for myocardial perfusion studies

Author

Radomír Chabiniok, Bruno Burtschell, Dominique Chapelle, and Philippe Moireau

Subjects
Poroelasticity, Biomechanical modeling, Computational physiology, Myocardial perfusion, Ischemic heart disease, Microvascular disease, Engineering (General). Civil engineering (General), TA1-2040
Abstract

In this paper, we adapt a previously developed poromechanical formulation to model the perfusion of myocardium during a cardiac cycle. First, a complete model is derived in 3D. Then, we perform a dimensional reduction under the assumption of spherical symmetry and propose a numerical algorithm that enables us to perform simulations of the myocardial perfusion throughout the cardiac cycle. These simulations illustrate the use of the proposed model to represent various physiological and pathological scenarios, specifically the vasodilation in the coronary network (to reproduce the standard clinical assessment of myocardial perfusion and perfusion reserve), the stenosis of a large coronary artery, an increased vascular resistance in the microcirculation (microvascular disease) and the consequences of inotropic activation (increased myocardial contractility) particularly at the level of the systolic flow impediment. Our results show that the model gives promising qualitative reproductions of complex physiological phenomena. This paves the way for future quantitative studies using clinical or experimental data.

Published
2022
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3. Sequential data assimilation for mechanical systems with complex image data: application to tagged-MRI in cardiac mechanics

Author

Alexandre Imperiale, Dominique Chapelle, and Philippe Moireau

Subjects
Data assimilation, Estimation, Cardiac modeling, Tagged-MRI, Patient-specific model, Mechanics of engineering. Applied mechanics, TA349-359, Systems engineering, TA168
Abstract

Abstract Tagged Magnetic Resonance images (tagged-MRI) are generally considered to be the gold standard of medical imaging in cardiology. By imaging spatially-modulated magnetizations of the deforming tissue, indeed, this modality enables an assessment of intra-myocardial deformations over the heart cycle. The objective of the present work is to incorporate the most valuable information contained in tagged-MRI in a data assimilation framework, in order to perform joint state-parameter estimation for a complete biomechanical model of the heart. This type of estimation is the second major step, after initial anatomical personalization, for obtaining a genuinely patient-specific model that integrates the individual characteristics of the patient, an essential prerequisite for benefitting from the model predictive capabilities. Here, we focus our attention on proposing adequate means of quantitatively comparing the cardiac model with various types of data that can be extracted from tagged-MRI after an initial image processing step, namely, 3D displacements fields, deforming tag planes or grids, or apparent 2D displacements. This quantitative comparison—called discrepancy measure—is then used to feed a sequential data assimilation procedure. In the state estimation stage of this procedure, we also propose a new algorithm based on the prediction–correction paradigm, which provides increased flexibility and effectiveness in the solution process. The complete estimation chain is eventually assessed with synthetic data, produced by running a realistic model simulation representing an infarcted heart characterized by increased stiffness and reduced contractility in a given region of the myocardium. From this simulation we extract the 3D displacements, tag planes and grids, and apparent 2D displacements, and we assess the estimation with each corresponding discrepancy measure. We demonstrate that—via regional estimation of the above parameters—the data assimilation procedure allows to quantitatively estimate the biophysical parameters with good accuracy, thus simultaneously providing the location of the infarct and characterizing its seriousness. This shows great potential for combining a biomechanical heart model with tagged-MRI in order to extract valuable new indices in clinical diagnosis.

Published
2021
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4. Thermodynamic properties of muscle contraction models and associated discrete-time principles

Author

François Kimmig, Dominique Chapelle, and Philippe Moireau

Subjects
Muscle contraction, Sliding filaments, Thermodynamically consistent time-discretization, Clausius–Duhem inequality, Mechanics of engineering. Applied mechanics, TA349-359, Systems engineering, TA168
Abstract

Abstract Considering a large class of muscle contraction models accounting for actin–myosin interaction, we present a mathematical setting in which solution properties can be established, including fundamental thermodynamic balances. Moreover, we propose a complete discretization strategy for which we are also able to obtain discrete versions of the thermodynamic balances and other properties. Our major objective is to show how the thermodynamics of such models can be tracked after discretization, including when they are coupled to a macroscopic muscle formulation in the realm of continuum mechanics. Our approach allows to carefully identify the sources of energy and entropy in the system, and to follow them up to the numerical applications.

Published
2019
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5. Dobutamine stress testing in patients with Fontan circulation augmented by biomechanical modeling.

Author

Bram Ruijsink, Konrad Zugaj, James Wong, Kuberan Pushparajah, Tarique Hussain, Philippe Moireau, Reza Razavi, Dominique Chapelle, and Radomír Chabiniok

Subjects
Medicine, Science
Abstract

Understanding (patho)physiological phenomena and mechanisms of failure in patients with Fontan circulation-a surgically established circulation for patients born with a functionally single ventricle-remains challenging due to the complex hemodynamics and high inter-patient variations in anatomy and function. In this work, we present a biomechanical model of the heart and circulation to augment the diagnostic evaluation of Fontan patients with early-stage heart failure. The proposed framework employs a reduced-order model of heart coupled with a simplified circulation including venous return, creating a closed-loop system. We deploy this framework to augment the information from data obtained during combined cardiac catheterization and magnetic resonance exams (XMR), performed at rest and during dobutamine stress in 9 children with Fontan circulation and 2 biventricular controls. We demonstrate that our modeling framework enables patient-specific investigation of myocardial stiffness, contractility at rest, contractile reserve during stress and changes in vascular resistance. Hereby, the model allows to identify key factors underlying the pathophysiological response to stress in these patients. In addition, the rapid personalization of the model to patient data and fast simulation of cardiac cycles make our framework directly applicable in a clinical workflow. We conclude that the proposed modeling framework is a valuable addition to the current clinical diagnostic XMR exam that helps to explain patient-specific stress hemodynamics and can identify potential mechanisms of failure in patients with Fontan circulation.

Published
2020
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6. Monitoring of cardiovascular physiology augmented by a patient-specific biomechanical model during general anesthesia. A proof of concept study.

Author

Arthur Le Gall, Fabrice Vallée, Kuberan Pushparajah, Tarique Hussain, Alexandre Mebazaa, Dominique Chapelle, Étienne Gayat, and Radomír Chabiniok

Subjects
Medicine, Science
Abstract

During general anesthesia (GA), direct analysis of arterial pressure or aortic flow waveforms may be inconclusive in complex situations. Patient-specific biomechanical models, based on data obtained during GA and capable to perform fast simulations of cardiac cycles, have the potential to augment hemodynamic monitoring. Such models allow to simulate Pressure-Volume (PV) loops and estimate functional indicators of cardiovascular (CV) system, e.g. ventricular-arterial coupling (Vva), cardiac efficiency (CE) or myocardial contractility, evolving throughout GA. In this prospective observational study, we created patient-specific biomechanical models of heart and vasculature of a reduced geometric complexity for n = 45 patients undergoing GA, while using transthoracic echocardiography and aortic pressure and flow signals acquired in the beginning of GA (baseline condition). If intraoperative hypotension (IOH) appeared, diluted norepinephrine (NOR) was administered and the model readjusted according to the measured aortic pressure and flow signals. Such patients were a posteriori assigned into a so-called hypotensive group. The accuracy of simulated mean aortic pressure (MAP) and stroke volume (SV) at baseline were in accordance with the guidelines for the validation of new devices or reference measurement methods in all patients. After NOR administration in the hypotensive group, the percentage of concordance with 10% exclusion zone between measurement and simulation was >95% for both MAP and SV. The modeling results showed a decreased Vva (0.64±0.37 vs 0.88±0.43; p = 0.039) and an increased CE (0.8±0.1 vs 0.73±0.11; p = 0.042) in hypotensive vs normotensive patients. Furthermore, Vva increased by 92±101%, CE decreased by 13±11% (p < 0.001 for both) and contractility increased by 14±11% (p = 0.002) in the hypotensive group post-NOR administration. In this work we demonstrated the application of fast-running patient-specific biophysical models to estimate PV loops and functional indicators of CV system using clinical data available during GA. The work paves the way for model-augmented hemodynamic monitoring at operating theatres or intensive care units to enhance the information on patient-specific physiology.

Published
2020
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17. Reduced left ventricular dynamics modeling based on a cylindrical assumption

Author

Martin Genet, Jérôme Diaz, Dominique Chapelle, Philippe Moireau, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)

Subjects
Computational Theory and Mathematics, Applied Mathematics, Modeling and Simulation, Computational mechanics, Continuum mechanics on manifold, Reduced-order modeling, Biomedical Engineering, [SPI.MECA.BIOM]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Biomechanics [physics.med-ph], Cardiac modeling, Molecular Biology, Software
Abstract

Biomechanical modeling and simulation is expected to play a significant role in the development of the next generation tools in many fields of medicine. However, full-fledged finite element models of complex organs such as the heart can be computationally very expensive, thus limiting their practical usability. Therefore, reduced models are much valuable to be used, e.g., for pre-calibration of full-fledged models, fast predictions, real-time applications, etc.. In this work, focused on the left ventricle, we develop a reduced model by defining reduced geometry & kinematics while keeping general motion and behavior laws, allowing to derive a reduced model where all variables & parameters have a strong physical meaning. More specifically, we propose a reduced ventricular model based on cylindrical geometry & kinematics, which allows to describe the myofiber orientation through the ventricular wall and to represent contraction patterns such as ventricular twist, two important features of ventricular mechanics. Our model is based on the original cylindrical model of [Guccione, McCulloch, & Waldman 1991; Guccione, Waldman, & McCulloch 1993], albeit with multiple differences: we propose a fully dynamical formulation, integrated into an open-loop lumped circulation model, and based on a material behavior that incorporates a fine description of contraction mechanisms; moreover, the issue of the cylinder closure has been completely reformulated; our numerical approach is novel as well, with consistent spatial (finite element) and time discretizations. Finally, we analyse the sensitivity of the model response to various numerical and physical parameters, and study its physiological response.

Published
2023
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24. Cardiosense3d: Patient-Specific Cardiac Simulation.

Author

Hervé Delingette, Maxime Sermesant, Jean-Marc Peyrat, Nicholas Ayache, Kawal S. Rhode, Reza Razavi, Elliot R. McVeigh, Dominique Chapelle, Jacques Sainte-Marie, Philippe Moireau, Miguel A. Fernández, Jean-Frédéric Gerbeau, Karima Djabella, Qinghua Zhang, and Michel Sorine

Published
2007
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27. Varying thin filament activation in the framework of the Huxley'57 model

Author

François Kimmig, Matthieu Caruel, Dominique Chapelle, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Laboratoire Modélisation et Simulation Multi-Echelle (MSME), and Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Centre National de la Recherche Scientifique (CNRS)-Université Gustave Eiffel

Subjects
Sarcomeres, Applied Mathematics, Biomedical Engineering, [SPI.MECA.BIOM]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Biomechanics [physics.med-ph], Cardiac modeling, Actins, Actin Cytoskeleton, Computational Theory and Mathematics, Thick and thin filament activation, Modeling and Simulation, Huxley'57 model, Calcium, Mathematical modeling, Molecular Biology, Software, Muscle Contraction
Abstract

International audience; Muscle contraction is triggered by the activation of the actin sites of the thin filament by calcium ions. It results that the thin filament activation level varies over time. Moreover, this activation process is also used as a regulation mechanism of the developed force. Our objective is to build a model of varying actin site activation level within the classical Huxley'57 two-state framework. This new model is obtained as an enhancement of a previously proposed formulation of the varying thick filament activation within the same framework [1]. We assume that the state of an actin site depends on whether it is activated and whether it forms a cross-bridge with the associated myosin head, which results in four possible states. The transitions between the actin site states are controlled by the global actin sites activation level and the dynamics of these transitions is coupled with the attachment-detachment process. A preliminary calibration of the model with experimental twitch contraction data obtained at varying sarcomere lengths is performed.

Published
2022
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29. Personalization of a cardiac electromechanical model using reduced order unscented Kalman filtering from regional volumes.

Author

Stéphanie Marchesseau, Hervé Delingette, Maxime Sermesant, Rocío Cabrera Lozoya, Catalina Tobon-Gomez, Philippe Moireau, Rosa M. Figueras i Ventura, Karim Lekadir, Alfredo I. Hernández, Mireille Garreau, Erwan Donal, Christophe Leclercq, Simon G. Duckett, Kawal S. Rhode, C. Aldo Rinaldi, Alejandro F. Frangi, Reza Razavi, Dominique Chapelle, and Nicholas Ayache

Published
2013
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34. Estimation of Regional Pulmonary Compliance in Idiopathic Pulmonary Fibrosis Based on Personalized Lung Poromechanical Modeling

Author

Cécile Patte, Pierre-Yves Brillet, Catalin Fetita, Jean-François Bernaudin, Thomas Gille, Hilario Nunes, Dominique Chapelle, Martin Genet, Laboratoire de mécanique des solides (LMS), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), Hypoxie et Poumon : pneumopathologies fibrosantes, modulations ventilatoires et circulatoires (H&P), UFR SMBH-Université Sorbonne Paris Nord, Hôpital Avicenne [AP-HP], Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP), Institut Polytechnique de Paris (IP Paris), Département Advanced Research And Techniques For Multidimensional Imaging Systems (TSP - ARTEMIS), Institut Mines-Télécom [Paris] (IMT)-Télécom SudParis (TSP), ARMEDIA (ARMEDIA-SAMOVAR), Services répartis, Architectures, MOdélisation, Validation, Administration des Réseaux (SAMOVAR), Institut Mines-Télécom [Paris] (IMT)-Télécom SudParis (TSP)-Institut Mines-Télécom [Paris] (IMT)-Télécom SudParis (TSP), Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), and ANR-19-CE45-0007,LungManyScale,Biomécanique Computationnelle Pulmonaire: Modélisation Multi-échelle et Estimation(2019)

Subjects
Physiology (medical), Biomedical Engineering, [SPI.MECA.BIOM]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Biomechanics [physics.med-ph], Humans, respiratory system, Tomography, X-Ray Computed, [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing, Lung, Idiopathic Pulmonary Fibrosis, respiratory tract diseases
Abstract

Pulmonary function is tightly linked to the lung mechanical behavior, especially large deformation during breathing. Interstitial lung diseases, such as idiopathic pulmonary fibrosis (IPF), have an impact on the pulmonary mechanics and consequently alter lung function. However, IPF remains poorly understood, poorly diagnosed, and poorly treated. Currently, the mechanical impact of such diseases is assessed by pressure–volume curves, giving only global information. We developed a poromechanical model of the lung that can be personalized to a patient based on routine clinical data. The personalization pipeline uses clinical data, mainly computed tomography (CT) images at two time steps and involves the formulation of an inverse problem to estimate regional compliances. The estimation problem can be formulated both in terms of “effective”, i.e., without considering the mixture porosity, or “rescaled,” i.e., where the first-order effect of the porosity has been taken into account, compliances. Regional compliances are estimated for one control subject and three IPF patients, allowing to quantify the IPF-induced tissue stiffening. This personalized model could be used in the clinic as an objective and quantitative tool for IPF diagnosis.

Published
2022
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35. Special Issue of the VPH2020 Conference: 'Virtual Physiological Human: When Models, Methods and Experiments Meet the Clinic'

Author

Irene E. Vignon-Clementel, Dominique Chapelle, Abdul I. Barakat, Aline Bel-Brunon, Philippe Moireau, Eric Vibert, SImulations en Médecine, BIOtechnologie et ToXicologie de systèmes multicellulaires (SIMBIOTX ), Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Laboratoire d'hydrodynamique (LadHyX), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS), Institut Polytechnique de Paris (IP Paris), Laboratoire de Mécanique des Contacts et des Structures [Villeurbanne] (LaMCoS), Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Physiopathologie et traitement des maladies du foie, Hôpital Paul Brousse-Institut National de la Santé et de la Recherche Médicale (INSERM)-Université Paris-Saclay, and Lamcos - gestionnaires Hal, Lamcos - gestionnaires Hal

Subjects
[SPI]Engineering Sciences [physics], [SPI] Engineering Sciences [physics], Biomedical Engineering, [INFO]Computer Science [cs], [INFO] Computer Science [cs], ComputingMilieux_MISCELLANEOUS
Abstract

International audience; No abstract available

Published
2022
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37. Time-Synchronization of Interventional Cardiovascular Magnetic Resonance Data Using a Biomechanical Model for Pressure-Volume Loop Analysis

Author

Maria Gusseva, Daniel A. Castellanos, Joshua S. Greer, Mohamed Abdelghafar Hussein, Keren Hasbani, Gerald Greil, Surendranath R. Veeram Reddy, Tarique Hussain, Dominique Chapelle, Radomír Chabiniok, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Boston Children's Hospital, Harvard Medical School [Boston] (HMS), University of Texas Southwestern Medical Center [Dallas], Kafrelsheikh University, and University of Texas at Austin [Austin]

Subjects
[SDV.MHEP.CSC]Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system, [SDV.IB.IMA]Life Sciences [q-bio]/Bioengineering/Imaging, Radiology, Nuclear Medicine and imaging, ComputingMilieux_MISCELLANEOUS
Abstract

International audience

Published
2022
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38. Prediction of Ventricular Mechanics After Pulmonary Valve Replacement in Tetralogy of Fallot by Biomechanical Modeling: A Step Towards Precision Healthcare

Author

Camille Hancock Friesen, Gerald F. Greil, Radomir Chabiniok, Maria Gusseva, Dominique Chapelle, Tarique Hussain, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), University of Texas Southwestern Medical Center [Dallas], University of Nebraska Medical Center, University of Nebraska System, Czech Technical University in Prague (CTU), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris)

Subjects
medicine.medical_specialty, medicine.medical_treatment, 0206 medical engineering, Biomedical Engineering, 02 engineering and technology, 030204 cardiovascular system & hematology, Contractility, 03 medical and health sciences, 0302 clinical medicine, Afterload, Valve replacement, [SDV.MHEP.CSC]Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system, Internal medicine, Pulmonary Valve Replacement, Medicine, ComputingMilieux_MISCELLANEOUS, Ventricular mechanics, Tetralogy of Fallot, business.industry, valvular heart disease, medicine.disease, 020601 biomedical engineering, 3. Good health, medicine.anatomical_structure, Ventricle, Cardiology, [SDV.IB]Life Sciences [q-bio]/Bioengineering, business, [SDV.MHEP]Life Sciences [q-bio]/Human health and pathology
Abstract

Clinical indicators of heart function are often limited in their ability to accurately evaluate the current mechanical state of the myocardium. Biomechanical modeling has been shown to be a promising tool in addition to clinical indicators. By providing a patient-specific measure of myocardial active stress (contractility), biomechanical modeling can enhance the precision of the description of patient’s pathophysiology at any given point in time. In this work we aim to explore the ability of biomechanical modeling to predict the response of ventricular mechanics to the progressively decreasing afterload in repaired tetralogy of Fallot (rTOF) patients undergoing pulmonary valve replacement (PVR) for significant residual right ventricular outflow tract obstruction (RVOTO). We used 19 patient-specific models of patients with rTOF prior to pulmonary valve replacement (PVR), denoted as PSMpre, and patient-specific models of the same patients created post-PVR (PSMpost)—both created in our previous published work. Using the PSMpre and assuming cessation of the pulmonary regurgitation and a progressive decrease of RVOT resistance, we built relationships between the contractility and RVOT resistance post-PVR. The predictive value of such in silico obtained relationships were tested against the PSMpost, i.e. the models created from the actual post-PVR datasets. Our results show a linear 1-dimensional relationship between the in silico predicted contractility post-PVR and the RVOT resistance. The predicted contractility was close to the contractility in the PSMpost model with a mean (± SD) difference of 6.5 (± 3.0)%. The relationships between the contractility predicted by in silico PVR vs. RVOT resistance have a potential to inform clinicians about hypothetical mechanical response of the ventricle based on the degree of pre-operative RVOTO.

Published
2021
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39. Biomechanical Modeling to Inform Pulmonary Valve Replacement in Tetralogy of Fallot Patients after Complete Repair

Author

Gerald F. Greil, Radomir Chabiniok, Keren Hasbani, Dominique Chapelle, Camille L. Hancock Friesen, Maria Gusseva, Animesh Tandon, Cécile Patte, Philippe Moireau, Tarique Hussain, Martin Genet, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), University of Texas Southwestern Medical Center [Dallas], University of Texas at Austin [Austin], Czech Technical University in Prague (CTU), King‘s College London, Guy's and St Thomas' Hospital [London], École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris

Subjects
Adult, Male, Reoperation, medicine.medical_specialty, Percutaneous, Heart Ventricles, 0206 medical engineering, Magnetic Resonance Imaging, Cine, 02 engineering and technology, 030204 cardiovascular system & hematology, Models, Biological, Article, Contractility, 03 medical and health sciences, 0302 clinical medicine, [SDV.MHEP.CSC]Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system, Cardiovascular modeling, Pulmonary Valve Replacement, Internal medicine, medicine.artery, Humans, Medicine, Abnormalities, Multiple, Cardiac Surgical Procedures, Retrospective Studies, Tetralogy of Fallot, Heart Valve Prosthesis Implantation, Cardiovascular magnetic resonance imaging, Pulmonary Valve, medicine.diagnostic_test, business.industry, Hemodynamics, Magnetic resonance imaging, Retrospective cohort study, Translational research, medicine.disease, 020601 biomedical engineering, Personalized medicine, Pulmonary Valve Insufficiency, Pulmonary artery, Cardiology, Female, Biomechanical model, [SDV.IB]Life Sciences [q-bio]/Bioengineering, Myocardial contractility, Cardiology and Cardiovascular Medicine, business, Follow-Up Studies
Abstract

BACKGROUND: A biomechanical model of the heart can be used to incorporate multiple data sources (electrocardiography, imaging, invasive hemodynamics). The purpose of this study was to use this approach in a cohort of patients with tetralogy of Fallot after complete repair (rTOF) to assess comparative influences of residual right ventricular outflow tract obstruction (RVOTO) and pulmonary regurgitation on ventricular health. METHODS: Twenty patients with rTOF who underwent percutaneous pulmonary valve replacement (PVR) and cardiovascular magnetic resonance imaging were included in this retrospective study. RESULTS: RV contractility before PVR (mean 66 ± kPa, mean ± standard deviation) was increased in patients with rTOF compared with normal RV (38–48 kPa) (P < 0.05). The contractility decreased significantly in all patients after PVR (P < 0.05). Patients with predominantly RVOTO demonstrated greater reduction in contractility (median decrease 35%) after PVR than those with predominant pulmonary regurgitation (median decrease 11%). The model simulated post-PVR decreased EDV for the majority and suggested an increase of Q(eff)—both in line with published data. CONCLUSIONS: This study used a biomechanical model to synthesize multiple clinical inputs and give an insight into RV health. Individualized modeling allows us to predict the RV response to PVR. Initial data suggest that residual RVOTO imposes greater ventricular work than isolated pulmonary regurgitation. Biomechanical models specific to individual patient and physiology (before and after PVR) were created and used to estimate the RV myocardial contractility. The ability of models to capture post-PVR changes of right ventricular (RV) end-diastolic volume (EDV) and effective flow in the pulmonary artery (Qeff) was also compared with expected values.

Published
2021
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40. Prediction of Ventricular Mechanics After Pulmonary Valve Replacement in Tetralogy of Fallot by Biomechanical Modeling: A Step Towards Precision Healthcare

Author

Maria, Gusseva, Tarique, Hussain, Camille, Hancock Friesen, Gerald, Greil, Dominique, Chapelle, and Radomír, Chabiniok

Subjects
Heart Valve Prosthesis Implantation, Pulmonary Valve, Postoperative Complications, Ventricular Remodeling, Predictive Value of Tests, Models, Cardiovascular, Tetralogy of Fallot, Humans, Precision Medicine, Biomechanical Phenomena, Ventricular Outflow Obstruction
Abstract

Clinical indicators of heart function are often limited in their ability to accurately evaluate the current mechanical state of the myocardium. Biomechanical modeling has been shown to be a promising tool in addition to clinical indicators. By providing a patient-specific measure of myocardial active stress (contractility), biomechanical modeling can enhance the precision of the description of patient's pathophysiology at any given point in time. In this work we aim to explore the ability of biomechanical modeling to predict the response of ventricular mechanics to the progressively decreasing afterload in repaired tetralogy of Fallot (rTOF) patients undergoing pulmonary valve replacement (PVR) for significant residual right ventricular outflow tract obstruction (RVOTO). We used 19 patient-specific models of patients with rTOF prior to pulmonary valve replacement (PVR), denoted as PSM

Published
2021

41. Hierarchical modeling of length-dependent force generation in cardiac muscles and associated thermodynamically-consistent numerical schemes

Author

Dominique Chapelle, Philippe Moireau, François Kimmig, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris)

Subjects
Computer science, Computational Mechanics, Ocean Engineering, Context (language use), multi-scale modeling, Sarcomere, biomechanics, 03 medical and health sciences, Myosin head, 0302 clinical medicine, numerical methods, 030304 developmental biology, 0303 health sciences, Frank–Starling law of the heart, Hierarchical modeling, Applied Mathematics, Mechanical Engineering, Numerical analysis, [SPI.MECA.BIOM]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Biomechanics [physics.med-ph], Cardiac modeling, Multiscale modeling, multiscale modeling, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, Computational Mathematics, Computational Theory and Mathematics, Coupling (computer programming), Frank-Starling mechanism, sarcomere, Biological system, 030217 neurology & neurosurgery, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

International audience; In the context of cardiac muscle modeling, the availability of the myosin heads in the sarcomeres varies over the heart cycle contributing to the Frank-Starling mechanism at the organ level. In this paper, we propose a new approach that allows to extend the Huxley'57 muscle contraction model equations to incorporate this variation. This extension is built in a thermodynamically consistent manner, and we also propose adapted numerical methods that satisfy thermodynamical balances at the discrete level. Moreover, this whole approach-both for the model and the numerics-is devised within a hierarchical strategy enabling the coupling of the microscopic sarcomere-level equations with the macroscopic tissue-level description. As an important illustration, coupling our model with a previously proposed simplified heart model, we demonstrate the ability of the modeling and numerical framework to capture the essential features of the Frank-Starling mechanism.

Published
2021
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42. Model-Assisted Time-Synchronization of Cardiac MR Image and Catheter Pressure Data

Author

Mohamed Abdelghafar Hussein, Maria Gusseva, Radomir Chabiniok, Surendranath R. Veeram Reddy, Gerald F. Greil, Daniel A. Castellanos, Joshua S. Greer, Tarique Hussain, Dominique Chapelle, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), University of Texas Southwestern Medical Center [Dallas], Boston Children's Hospital, Pediatric department, Kafrelsheikh University, Kafrelsheikh University, École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, and Faculty of Medicine, Kafrelsheikh University, Kafrelsheikh, Egypt

Subjects
Physics, cardiovascular modeling, time-synchronization of clinical data, medicine.diagnostic_test, Cardiac cycle, pressure volume loops, Image (category theory), Magnetic resonance imaging, personalized medicine, 030204 cardiovascular system & hematology, Type (model theory), 030218 nuclear medicine & medical imaging, 03 medical and health sciences, QRS complex, 0302 clinical medicine, Nuclear magnetic resonance, translational research, [SDV.MHEP.CSC]Life Sciences [q-bio]/Human health and pathology/Cardiology and cardiovascular system, Norm (mathematics), Ventricular pressure, medicine, [SDV.IB]Life Sciences [q-bio]/Bioengineering, interventional cardiovascular magnetic resonance imaging, Volume (compression)
Abstract

International audience; When combining cardiovascular magnetic resonance imaging (CMR) with pressure catheter measurements, the acquired imageand pressure data need to be synchronized in time. The time offset between the image and pressure data depends on a number of factors,such as the type and settings of the MR sequence, duration and shape of QRS complex or the type of catheter, and cannot be typically estimated beforehand. In the present work we propose using a biophysical heart model to synchronize the left ventricular (LV) pressure and volume (P-V) data. Ten patients, who underwent CMR and LV catheterization, were included. A biophysical model of reduced geometrical complexity with physiologically substantiated timing of each phase of the cardiac cycle was first adjusted to individual patients using basic morphological and functional indicators. The pressure and volume waveforms simulated by the patient-specific models were then used as templates to detect the time offset between the acquired ventricular pressure and volume waveforms. Time-varying ventricular elastance was derived from clinical data both as originally acquired as well as when time-synchronized, and normalized with respect to end-systolic time and maximum elastance value$E^N_\text {orig}(t)$, $E^N_\text {t-syn}(t)$, respectively). $E^N_\text {t-syn}(t)$ was significantly closer to the experimentally obtained $E^N_\text {exp}(t)$ published in the literature (p < 0.05, $L^2$ norm). The work concludes that the model-driven time-synchronization of P-V data obtained by catheter measurement and CMR allows to generate high quality P-V loops, which can then be used for clinical interpretation.

Published
2021
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43. Sequential data assimilation for mechanical systems with complex image data: application to tagged-MRI in cardiac mechanics

Author

Philippe Moireau, Dominique Chapelle, Alexandre Imperiale, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Département Imagerie et Simulation pour le Contrôle (DISC), Laboratoire d'Intégration des Systèmes et des Technologies (LIST (CEA)), Direction de Recherche Technologique (CEA) (DRT (CEA)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Direction de Recherche Technologique (CEA) (DRT (CEA)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay, École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, and Laboratoire d'Intégration des Systèmes et des Technologies (LIST)

Subjects
Computer science, 0206 medical engineering, Image processing, 02 engineering and technology, Data type, Synthetic data, 030218 nuclear medicine & medical imaging, lcsh:TA168, 03 medical and health sciences, 0302 clinical medicine, Data assimilation, Medical imaging, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Engineering (miscellaneous), Flexibility (engineering), Measure (data warehouse), Tagged-MRI, business.industry, Applied Mathematics, Pattern recognition, Cardiac modeling, 020601 biomedical engineering, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, Computer Science Applications, lcsh:Systems engineering, Modeling and Simulation, Patient-specific model, Artificial intelligence, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Focus (optics), business, lcsh:Mechanics of engineering. Applied mechanics, lcsh:TA349-359, Estimation
Abstract

Tagged Magnetic Resonance images (tagged-MRI) are generally considered to be the gold standard of medical imaging in cardiology. By imaging spatially-modulated magnetizations of the deforming tissue, indeed, this modality enables an assessment of intra-myocardial deformations over the heart cycle. The objective of the present work is to incorporate the most valuable information contained in tagged-MRI in a data assimilation framework, in order to perform joint state-parameter estimation for a complete biomechanical model of the heart. This type of estimation is the second major step, after initial anatomical personalization, for obtaining a genuinely patient-specific model that integrates the individual characteristics of the patient, an essential prerequisite for benefitting from the model predictive capabilities. Here, we focus our attention on proposing adequate means of quantitatively comparing the cardiac model with various types of data that can be extracted from tagged-MRI after an initial image processing step, namely, 3D displacements fields, deforming tag planes or grids, or apparent 2D displacements. This quantitative comparison—called discrepancy measure—is then used to feed a sequential data assimilation procedure. In the state estimation stage of this procedure, we also propose a new algorithm based on the prediction–correction paradigm, which provides increased flexibility and effectiveness in the solution process. The complete estimation chain is eventually assessed with synthetic data, produced by running a realistic model simulation representing an infarcted heart characterized by increased stiffness and reduced contractility in a given region of the myocardium. From this simulation we extract the 3D displacements, tag planes and grids, and apparent 2D displacements, and we assess the estimation with each corresponding discrepancy measure. We demonstrate that—via regional estimation of the above parameters—the data assimilation procedure allows to quantitatively estimate the biophysical parameters with good accuracy, thus simultaneously providing the location of the infarct and characterizing its seriousness. This shows great potential for combining a biomechanical heart model with tagged-MRI in order to extract valuable new indices in clinical diagnosis.

Published
2021
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44. A quasi-static poromechanical model of the lungs

Author

Cécile Patte, Martin Genet, Dominique Chapelle, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), ANR-10-EQPX-0037,MATMECA,MATériaux-MECAnique/Elaboration-Caractérisation-Observation-Modélisation-Simulation(2010), ANR-19-CE45-0007,LungManyScale,Biomécanique Computationnelle Pulmonaire: Modélisation Multi-échelle et Estimation(2019), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris)

Subjects
Mechanical Engineering, Respiration, 0206 medical engineering, Diaphragm, Poromechanics, Modeling, [SPI.MECA.BIOM]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Biomechanics [physics.med-ph], 02 engineering and technology, 020601 biomedical engineering, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, 030218 nuclear medicine & medical imaging, 03 medical and health sciences, 0302 clinical medicine, Inverse Poromechanics, Modeling and Simulation, Finite Element Method, Pulmonary Mechanics, [SDV.MHEP.AHA]Life Sciences [q-bio]/Human health and pathology/Tissues and Organs [q-bio.TO], Lung, Biotechnology
Abstract

International audience; The lung vital function of providing oxygen to the body heavily relies on its mechanical behavior, and the interaction with its complex environment. In particular, the large compliance and the porosity of the pulmonary tissue are critical for lung inflation and air inhalation, and the diaphragm, the pleura, the rib cage and intercostal muscles all play a role in delivering and controlling the breathing driving forces. In this paper, we introduce a novel poromechanical model of the lungs. The constitutive law is derived within a general poromechanics theory via the formulation of lung-specific assumptions, leading to a hyperelastic potential reproducing the volume response of the pulmonary mixture to a change of pressure. Moreover, physiological boundary conditions are formulated to account for the interaction of the lungs with their surroundings, including a following pressure and bilateral frictionless contact. A strategy is established to estimate the unloaded configuration from a given loaded state, with a particular focus on ensuring a positive porosity. Finally, we illustrate through several realistic examples the relevance of our model and its potential clinical applications.

Published
2021
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45. Combining data assimilation and machine learning to build data-driven models for unknown long time dynamics—Applications in cardiovascular modeling

Author

Francesco Regazzoni, Philippe Moireau, Dominique Chapelle, Modeling and Scientific Computing [Milano] (MOX), Politecnico di Milano [Milan] (POLIMI), Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris

Subjects
cardiovascular modeling, Computer science, Differential equation, data‐driven modeling, 0206 medical engineering, Biomedical Engineering, Context (language use), 02 engineering and technology, 030204 cardiovascular system & hematology, Machine learning, computer.software_genre, Field (computer science), Data-driven, 03 medical and health sciences, 0302 clinical medicine, multiscale problems, Molecular Biology, data assimilation, Interpretability, Parametric statistics, Research Article ‐ Fundamental, Artificial neural network, business.industry, Applied Mathematics, Models, Theoretical, 020601 biomedical engineering, Test case, machine learning, Computational Theory and Mathematics, data-driven modeling, Modeling and Simulation, Artificial intelligence, business, computer, artificial neural networks, Algorithms, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Software
Abstract

We propose a method to discover differential equations describing the long‐term dynamics of phenomena featuring a multiscale behavior in time, starting from measurements taken at the fast‐scale. Our methodology is based on a synergetic combination of data assimilation (DA), used to estimate the parameters associated with the known fast‐scale dynamics, and machine learning (ML), used to infer the laws underlying the slow‐scale dynamics. Specifically, by exploiting the scale separation between the fast and the slow dynamics, we propose a decoupling of time scales that allows to drastically lower the computational burden. Then, we propose a ML algorithm that learns a parametric mathematical model from a collection of time series coming from the phenomenon to be modeled. Moreover, we study the interpretability of the data‐driven models obtained within the black‐box learning framework proposed in this paper. In particular, we show that every model can be rewritten in infinitely many different equivalent ways, thus making intrinsically ill‐posed the problem of learning a parametric differential equation starting from time series. Hence, we propose a strategy that allows to select a unique representative model in each equivalence class, thus enhancing the interpretability of the results. We demonstrate the effectiveness and noise‐robustness of the proposed methods through several test cases, in which we reconstruct several differential models starting from time series generated through the models themselves. Finally, we show the results obtained for a test case in the cardiovascular modeling context, which sheds light on a promising field of application of the proposed methods., We propose a method to discover differential equations describing the long‐term dynamics of phenomena featuring a multiscale behavior in time, starting from measurements taken at the fast‐scale. Our methodology is based on a synergetic combination of data assimilation, used to estimate the parameters associated with the known fast‐scale dynamics, and machine learning, used to infer the laws underlying the slow‐scale dynamics. By exploiting the scale separation between the fast and the slow dynamics, we propose a decoupling of time scales that allows to drastically lower the computational burden.

Published
2021
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46. Personalized pulmonary poromechanics

Author

Pierre-Yves Brillet, Dominique Chapelle, Catalin Fetita, Cécile Patte, Martin Genet, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Institut Polytechnique de Paris (IP Paris), Département Advanced Research And Techniques For Multidimensional Imaging Systems (TSP - ARTEMIS), Institut Mines-Télécom [Paris] (IMT)-Télécom SudParis (TSP), ARMEDIA (ARMEDIA-SAMOVAR), Services répartis, Architectures, MOdélisation, Validation, Administration des Réseaux (SAMOVAR), Institut Mines-Télécom [Paris] (IMT)-Télécom SudParis (TSP)-Institut Mines-Télécom [Paris] (IMT)-Télécom SudParis (TSP), Hypoxie et Poumon : pneumopathologies fibrosantes, modulations ventilatoires et circulatoires (H&P), UFR SMBH-Université Sorbonne Paris Nord, École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, and Département Advanced Research And Techniques For Multidimensional Imaging Systems (ARTEMIS)

Subjects
Computer science, 0206 medical engineering, Poromechanics, Biomedical Engineering, Bioengineering, 02 engineering and technology, [SDV.MHEP.PSR]Life Sciences [q-bio]/Human health and pathology/Pulmonology and respiratory tract, 03 medical and health sciences, 0302 clinical medicine, Pulmonary mechanics, Modeling, [SPI.MECA.BIOM]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Biomechanics [physics.med-ph], Control engineering, 030229 sport sciences, General Medicine, respiratory system, 020601 biomedical engineering, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, 3. Good health, Computer Science Applications, Human-Computer Interaction, Current (fluid), Estimation, Simulation
Abstract

International audience; Lung biomechanics has been extensively studied by physiologists, experimentally as well as theoretically, laying the ground for our current fundamental understanding of the relationship between function and mechanical behavior. However, many questions remain, notably in the intricate coupling between the multiple constituents. These fundamental questions represent real clinical challenges, as pulmonary diseases are an important health burden. Interstitial lung diseases, for instance, affect several million people globally. Idiopathic Pulmonary Fibrosis (IPF), notably, a progressive form of interstitial lung diseases where some alveolar septa get thicker and stiffer while others get completely damaged, remains poorly understood, poorly diagnosed, and poorly treated (Nunes et al. 2015).

Published
2020
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47. Stochastic modeling of chemical–mechanical coupling in striated muscles

Author

Dominique Chapelle, Philippe Moireau, Matthieu Caruel, Laboratoire de Modélisation et Simulation Multi Echelle (MSME), Université Paris-Est Marne-la-Vallée (UPEM)-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Centre National de la Recherche Scientifique (CNRS), Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Université Paris-Saclay, Centre National de la Recherche Scientifique (CNRS)-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Université Paris-Est Marne-la-Vallée (UPEM), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris

Subjects
Mechanical Phenomena, power stroke, 0206 medical engineering, Probability density function, 02 engineering and technology, Myosins, Models, Biological, Sarcomere, Myosin head, [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph], Isometric Contraction, [SDV.MHEP.PHY]Life Sciences [q-bio]/Human health and pathology/Tissues and Organs [q-bio.TO], muscle modeling, sliding filament, Statistical physics, [PHYS.MECA.BIOM]Physics [physics]/Mechanics [physics]/Biomechanics [physics.med-ph], Power stroke, Physics, Coupling, Stochastic Processes, Partial differential equation, Viscosity, Mechanical Engineering, 020601 biomedical engineering, Muscle, Striated, Biomechanical Phenomena, Macroscopic scale, Modeling and Simulation, Calibration, Thermodynamics, cross-bridge, sarcomere, Langevin equations, Fokker-Planck equations, Biotechnology
Abstract

International audience; We propose a chemical-mechanical model of myosin heads in sarcomeres, within the classical description of rigid sliding filaments. In our case, myosin heads have two mechanical degrees-of-freedom (dofs) - one of which associated with the so-called power stroke - and two possible chemical states, i.e. bound to an actin site or not. Our major motivations are twofold: (1) to derive a multiscale coupled chemical-mechanical model, and (2) to thus account - at the macroscopic scale - for mechanical phenomena that are out of reach for classical muscle models. This model is first written in the form of Langevin stochastic equations, and we are then able to obtain the corresponding Fokker-Planck partial differential equations governing the probability density functions associated with the mechanical dofs and chemical states. This second form is important, as it allows to monitor muscle energetics, and also to compare our model with classical ones, such as the Huxley'57 model to which our equations are shown to reduce under two different types of simplifying assumptions. This provides insight, and gives a Langevin form for Huxley'57. We then show how we can calibrate our model based on experimental data - taken here for skeletal muscles - and numerical simulations demonstrate the adequacy of the model to represent complex physiological phenomena, in particular the fast isometric transients in which the power stroke is known to have a crucial role, thus circumventing a limitation of many classical models.

Published
2019
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48. CardioSense3D.

Author

Hervé Delingette, Maxime Sermesant, Nicholas Ayache, Dominique Chapelle, Miguel A. Fernández, Jean-Frédéric Gerbeau, and Michel Sorine

Published
2007

49. Activation-CONTRACTION COUPLING IN A MULTISCALE HEART MODEL

Author

François Kimmig, Matthieu Caruel, Dominique Chapelle, Philippe Moireau, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Modélisation et Simulation Multi Echelle (MSME), Université Paris-Est Marne-la-Vallée (UPEM)-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Centre National de la Recherche Scientifique (CNRS), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Université Paris-Est Marne-la-Vallée (UPEM), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), and Caruel, Matthieu

Subjects
[PHYS.MECA.SOLID] Physics [physics]/Mechanics [physics]/Solid mechanics [physics.class-ph], [PHYS.MECA.SOLID]Physics [physics]/Mechanics [physics]/Solid mechanics [physics.class-ph], [PHYS.MECA.BIOM] Physics [physics]/Mechanics [physics]/Biomechanics [physics.med-ph], [PHYS.MECA.BIOM]Physics [physics]/Mechanics [physics]/Biomechanics [physics.med-ph], [PHYS.MECA.SOLID]Physics [physics]/Mechanics [physics]/Mechanics of the solides [physics.class-ph], ComputingMilieux_MISCELLANEOUS
Abstract

International audience

Published
2019

50. Cardiac displacement tracking with data assimilation combining a biomechanical model and an automatic contour detection

Author

Gautier Bureau, Dominique Chapelle, Jürgen Weese, Jaroslav Tintera, Radomir Chabiniok, Alexandra Groth, Philippe Moireau, Mathematical and Mechanical Modeling with Data Interaction in Simulations for Medicine (M3DISIM), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), King‘s College London, Philips Research [Germany], Philips Research, Institute for Clinical and Experimental Medicine (IKEM), Zemzemi, Nejib, Ozenne, Valéry, Vigmond, Edward, Coudière, Yves, École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris)

Subjects
Computational model, Computer science, business.industry, [SDV.IB.IMA]Life Sciences [q-bio]/Bioengineering/Imaging, 0206 medical engineering, 02 engineering and technology, Tracking (particle physics), 020601 biomedical engineering, Biophysical heart modeling, cine MRI, Displacement (vector), Bottleneck, 030218 nuclear medicine & medical imaging, Term (time), Cine mri, 03 medical and health sciences, 0302 clinical medicine, Data assimilation, Computer vision, Artificial intelligence, business, [SDV.IB.BIO]Life Sciences [q-bio]/Bioengineering/Biomaterials, Cardiac imaging
Abstract

International audience; Data assimilation in computational models represents an essential step in building patient-specific simulations. This work aims at circumventing one major bottleneck in the practical use of data assimilation strategies in cardiac applications, namely, the difficulty of formulating and effectively computing adequate data-fitting term for cardiac imaging such as cine MRI. We here provide a proof-of-concept study of data assimilation based on automatic contour detection. The tissue motion simulated by the data assimilation framework is then assessed with displacements extracted from tagged MRI in six subjects, and the results illustrate the performance of the proposed method, including for circumferential displacements, which are not well extracted from cine MRI alone.

Published
2019
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